Getting to convince your parents to let you have a boyfriend takes a lot of courage and it's tough when you have strict parents. Follow these tips and good luck!

[edit] Steps

Come out straight and tell your parents you need to talk. Say this confidently. Make sure your parents are in a happy mood or either really busy.
Tell your parents that you have thought this through and that they should respect your opinion. Also tell them you respect their opinion.
Present your case and tell them that there is a boy you would like to date.
Tell them that you think you are old and mature enough to date the person you like, and that you will be careful in every situation if they just give you a chance and trust you on this decision. One needs to have ready concrete examples of why they think they are mature enough to date. Does the child/teen help with housework? Do they do it without the parents having to ask? Does the child do (and finish) their homework without being asked? Does the child finish their homework before doing free time?
- If your parents say no right away, ask them "why?" in a calm manner. Have a disappointed, sad look on your face, but don't cry. That's a sign of weakness to most parents, and acting immature is not going to help you win your parents' approval.
Tell them about the boy. Tell them about his personality, what kind of grades does he get in school, his job, what he wants to be when he grows up, his family and other things. This will let them know about him. Suggest they meet the guy you like first and see how he is and let them decide then.
Tell them that you will be responsible with your actions and that you will suffer the consequences if anything bad happens.
Respond to their final answer maturely:
- If your parents say yes, and give your parents a hug and a kiss to show your affection and happiness!
- If your parents still stay no, try asking again or just wait until the time comes for you to date. Or ask your parents if you can go on a group date with your friends and your crush. With this, your parents will feel more comfortable since you will be with other friends, rather than alone with your crush.

[edit] Tips

The best time to ask your parents is when they are in a good mood. Not, for example, after you failed a test.
Stay calm throughout the discussion until your parents say yes. Then you can let your happiness out.
Update your parents on dates. They'll feel more secure about you having a boyfriend and will give you more privacy later on.
Try going on a double date with your parents. It can be embarrassing, but it will show them what you and your soon-to-be boyfriend do when you two are out on a date.
Be mature. Do not whine and yell at them why can't you have a boyfriend. This will make them think you are never going to grow up and not being able to handle a boyfriend.
Invite your friends over to your house and let them talk to your parents about the boy. It will make the rope less and less tighter if you have other people there to support your choice.
Have the parents of the boy come to dinner with your family. Show them what kind of a family he has and what environment they let him grow up in.